Finite Group DatabasebetaFinite Group Databasebeta| order | 1024 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C26×C42 |
| direct product | C2×#346276 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23 | #2840 |
| commutator, Frattini, cosocle | C25 | C25 |
| prime radical | C23×#120 | C22 |
| LCS | G ▷ C25 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23 ◁ C26 ◁ G | |
| LECS | G ▷ C25 ▷ C22 ▷ C1 | |
7459 conjugacy classes of subgroups; only the 501 normal subgroups are shown.
This group has 7459 conjugacy classes of subgroups — too many to draw. Only its 501 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 64 |
64 conjugacy classes — view the full character table.
| Fitting subgroup of | C2×#72340913 |
| maximal subgroup of | C2×#72340913, #72341124 |
| maximal normal subgroup of | C2×#72340913, #72341124 |
Past the SmallGroups library coverage — no SmallGroups id.